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strong coloring
Strong colorability ★★★
Author(s): Aharoni; Alon; Haxell
Let be a positive integer. We say that a graph
is strongly
-colorable if for every partition of the vertices to sets of size at most
there is a proper
-coloring of
in which the vertices in each set of the partition have distinct colors.
Conjecture If
is the maximal degree of a graph
, then
is strongly
-colorable.
![$ \Delta $](/files/tex/e3f8e135c571143e94f1d4f236326b862080b200.png)
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
![$ 2 \Delta $](/files/tex/853908c29bc170f3b27832e4df3751c7626ff012.png)
Keywords: strong coloring
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